When I\'m observing a bright object like a planet, I see an opposing ghost image. What causes that?

The ghost image, and it\'s evil twin, the out-of-focus ghost is caused by internal reflections inside the eyepiece. The only way to eliminate these is to eliminate air-spaces in the eyepieces, as the ghost is caused by a double bounce between two lenses in close proximity. While the ghost is an annoyance, the out of focus ghost is more of an enemy, as it reduces overall contrast of the image, which determines how much detail you\'ll be able to see. The treatment, if not eh cure, is di-electric multicoating of the lens-facing surfaces inside the eyepiece.